Classification of almost Yamabe solitons in Euclidean spaces

TL;DR

This paper classifies almost Yamabe solitons on hypersurfaces in Euclidean spaces and explores related solitons with concurrent vector fields, providing comprehensive results on their geometric structures and classifications.

Contribution

It offers a complete classification of almost Yamabe solitons in Euclidean spaces and extends results to Yamabe solitons and Ricci solitons on submanifolds.

Findings

Complete classification of almost Yamabe solitons in Euclidean spaces

Results on almost Yamabe solitons with concurrent vector fields

Classification of Ricci solitons on minimal submanifolds

Abstract

In this paper, we completely classify almost Yamabe solitons on hypersurfaces in Euclidean spaces arisen from the position vector field. Some results of almost Yamabe solitons with a concurrent vector field and almost Yamabe solitons on submanifolds in Riemannian manifolds equipped with a concurrent vector field are also presented. Moreover, we classify complete Ricci solitons on minimal submanifolds in non-positively curved space forms. For almost Yamabe solitons, all of results in this paper can be applied to Yamabe solitons.